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Abstract

An efficient algorithm for calculating nonparaxial scalar field distributions in the focal region of a lens is discussed. The algorithm is based on fast Fourier transform implementations of the first Rayleigh–Sommerfeld diffraction integral and assumes that the input field at the pupil plane has a larger extent than the field in the focal region. A sampling grid is defined over a finite region in the output plane and referred to as a tile. The input field is divided into multiple separate spatial regions of the size of the output tile. Finally, the input tiles are added coherently to form a summed tile, which is propagated to the output plane. Since only a single tile is propagated, there are significant reductions of computational load and memory requirements. This method is combined either with a subpixel sampling technique or with a chirp z-transform to realize smaller sampling intervals in the output plane than in the input plane. For a given example the resulting methods enable a speedup of approximately 800× in comparison to the normal angular spectrum method, while the memory requirements are reduced by more than 99%.

References

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a The core parts of the algorithms were timed separately from each other. Additional functions like fftshift were not considered. The results are presented for the AS.b Estimations based on calculations with N=32768.